Oberwolfach Surgery Seminar 2012: General information
m |
m |
||
Line 1: | Line 1: | ||
− | <!--* [[Oberwolfach Surgery Seminar 2012: Program|Program]] --> | + | <!--* [[Oberwolfach Surgery Seminar 2012: Program|Program]] --><!-- * [[Oberwolfach Surgery Seminar 2012: Exercises|Exercises]] -->* [[Oberwolfach Surgery Seminar 2012: Glossary|Glossary]] |
− | <!-- * [[Oberwolfach Surgery Seminar 2012: Exercises|Exercises]] --> | + | |
− | * [[Oberwolfach Surgery Seminar 2012: Glossary|Glossary]] | + | |
* [[:Category:Surgery|Surgery on the Manifold Atlas]] | * [[:Category:Surgery|Surgery on the Manifold Atlas]] | ||
== Prerequisites == | == Prerequisites == |
Revision as of 16:58, 17 April 2012
Contents |
1 Prerequisites
The prerequisites for the seminar are a solid knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, generalized homology and cohomology, homotopy groups.
Participants should be familiar with the ideas covered in the first 7 chapters of the book [Ranicki2002]. However material from sections 2.2., 4.2, 5.4, 7.3 will be covered during the seminar. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is A. Hatcher, Algebraic topology, Cambridge University Press, 2002. MR1867354 (2002k:55001) Zbl 1044.55001.
The main references for the material covered in the seminar are [Ranicki1979], [Ranicki1992], [Kühl&Macko&Mole2011] and [Wall1999].
2 Schedule
2.1 Geometric surgery
- Bundle theories DC
- Spivak normal fibration DC
- Normal invariants and surgery below the middle dimension DC
- L-groups of rings with involution DC
- Surgery obstructions DC
- The geometric surgery exact sequence DC
- The TOP surgery exact sequence TM
2.2 Algebraic surgery
- Structured chain complexes AR
- Symmetric and quadratic signature AR
- Algebraic surgery and L-groups via chain complexes AR
- Examples of Poincaré complexes Speakers TBA
- Algebraic bordism categories and categories over complexes TM
- Generalized homology theories TM
- The normal complexes TM
2.3 Algebraic surgery versus geometric surgery
- The algebraic surgery exact sequence TM
- The topological block bundle obstruction TM
- The surgery obstruction AR
- The geometric and algebraic surgery exact sequences AR
- Examples and related developments AR